What is the sum from n=0 to infinity of (i/3)^n ?

The sum from n=0 to infinity of (i/3)^n is converges

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sum from n=0 to infinity of (i/3)^n

n = 0 \sum \infty (\frac{i}{3})^{n}

converges

Solution steps

n = 0 \sum \infty (\frac{i}{3})^{n}

Apply Series Ratio Test:

converges

= converges

\frac{d}{d x} (2 (1 - x)^{- 3})

x \to 0 lim (\frac{5 ^{x} - 4 ^{x}}{x})

\frac{2 x + 3}{3 x + 2}

\int_{0}^{1} \frac{z}{( z ^{2} + 1 ) ^{3}} d z

x \to 0 + lim (ln (x^{3}))

What is the sum from n=0 to infinity of (i/3)^n ?
The sum from n=0 to infinity of (i/3)^n is converges